1. Technical Field
The present invention relates to a position control apparatus for a feed-axis (i.e., a driven member, such as a table, a saddle, or a spindle head) of a machine tool or the like. More specifically, the present invention relates to an improved position control apparatus capable of realizing full-closed control in controlling the position of a driven member based on a position command value.
2. Related Art
The following conventional techniques are available to reduce a position error in a position control apparatus that includes a linear scale attached to a movable portion of a machine tool to detect the position of a driven member and performs full-closed control based on a comparison between a detected driven member position and a position command value.
To reduce the position error in a transient response, it is useful to set the gain of a speed loop and the gain of a position loop to higher values. In this case, the driven member can be accurately controlled in such a way as to reduce adverse influence of an unpredictable load change or disturbance, such as a change in sliding friction of the movable portion or a cutting load.
FIG. 5 is a block diagram illustrating a general full-closed control system. A linear scale 11 generates a position detection value Pl that represents the position of a driven member 12. A subtracter 2 receives the position detection value Pl, as a position feedback value, and calculates a deviation Pdif of the position detection value Pl relative to a position command Pc.
A speed command calculator 3 multiplies the position deviation Pdif by a proportional gain Kp and outputs a multiplication result as a speed command Vc. Meanwhile, a differentiator 14 differentiates a position detection value Pm obtained by a position detector 9 attached to a motor 10. The differentiator 14 outputs a differentiation result as a motor speed detection value Vm. A subtracter 4 obtains a deviation of the motor speed detection value Vm relative to the speed command Vc and outputs the obtained deviation as a speed deviation.
A torque command calculator (i.e., speed loop proportional gain) 5 outputs a speed deviation proportional component based on the speed deviation received from the subtracter 4 and a speed loop proportional gain Pv. A torque command calculator (i.e., speed loop integral gain) 6 outputs a speed deviation integral component based on the speed deviation and a speed loop integral gain Iv. An adder 7 adds the speed deviation proportional component and the speed deviation integral component, and outputs an addition result as a torque command Tc. Further, a portion 8 illustrated in FIG. 5 includes various filters capable of filtering the torque command Tc, and a current control unit.
In the present example, a simplified model is provided based on an assumption that the transfer characteristic of a portion ranging from the speed command Vc to the motor speed detection value Vm is equal to 1. The driven member 12 is connected to the motor via a spring having a spring constant Kb. M represents the weight of the driven member. D represents a viscous friction coefficient of the driven member. In this case, the block diagram illustrated in FIG. 5 can be replaced by a block diagram illustrated in FIG. 6. The transfer function of the entire control system can be expressed using the following formula (1). In formula (1), S represents a Laplacian operator.Pl(S)/Pc(S)=Kp·Kb/(M·S3+D·S2+Kb·S+Kp·Kb)   formula (1)
FIG. 10 is a gain diagram illustrating a characteristic of the entire control system if a condition Kp<<(Kb/M)1/2 is applied to the above-described formula.
Recent developments in various filtering techniques or damping controls and introduction of improved speed loops have enabled setting of high values in position/speed loop gain setting. However, the rigidity of a working part of the feed-axis may decrease due to aging (e.g., frictional wear and looseness) of a component that constitutes a driving mechanism, or due to reduction in tensile strength of a ball screw that is derived from expansion of the ball screw, which may occur when the temperature increases during a continuous operation. In this case, the mechanical resonance frequency (Kb/M)1/2 decreases. FIG. 11 is a diagram illustrating a gain characteristic of the entire control system defined by formula (1) in the above-described case.
More specifically, a gain margin of the mechanical resonance frequency (Kb/M)1/2 decreases due to a highly set position loop gain. In some cases, a driven member may vibrate at low frequencies. Further, in a large-scale machining center, the mechanical resonance frequency (Kb/M)1/2 decreases if a workpiece mounted on a driven member is heavier than the expected value. Therefore, low frequency vibrations occur similarly. To solve the above-described problem, the following technique is conventionally available.
FIG. 7 is a control block diagram illustrating another conventional position control apparatus that is directed to suppression of low frequency vibrations. Components similar to those illustrated in FIG. 5 are denoted by the same reference numerals and their descriptions are not repeated. A position detection value calculator 20 illustrated in FIG. 7 outputs a position feedback value Pd, which represents the position defined by the following formula (2) including the driven member position detection value Pl and the motor position detection value Pm. In formula (2), Tp represents a time constant of a first-order delay circuit 17 and S represents a Laplacian operator.Pd=Pm+(Pl−Pm)/(1+Tp·S)   formula (2)
In formula (2), 1/(1+Tp·S) represents the first-order delay circuit. The first-order delay circuit 17 illustrated in FIG. 7 calculates the second term of formula (2).
A dotted line in FIG. 12 indicates a gain characteristic of the entire control system illustrated in FIG. 7 in a case where a condition Tp>>(Kb/M)1/2 is applied to formula (2). The gain margin of the mechanical resonance frequency (Kb/M)1/2 becomes larger. Further, a solid line in FIG. 12 indicates a gain characteristic of the entire control system in a case where the rigidity of a working part of the feed-axis decreases. Thus, the conventional position control apparatus illustrated in FIG. 7 is effective in solving the problem of low frequency vibrations described in the conventional example illustrated in FIG. 5.
FIG. 8 is a control block diagram illustrating another position control apparatus that is directed to suppress low frequency vibrations. Components similar to those illustrated in FIG. 5 are denoted by the same reference numerals and their descriptions are not repeated. A speed detection value calculator 25 outputs a speed feedback value Vd, which represents the speed defined by the following formula (3), including a driven member speed detection value Vl (i.e., a value obtained by a differentiator 21 that differentiates the driven member position detection value Pl) and the motor speed detection value Vm. In formula (3), Tv represents a time constant of a first-order delay circuit 23 and S represents a Laplacian operator.Vd=Vm+(Vl−Vm)/(1+Tv·S)   formula (3)
In formula (3), 1/(1+Tv·S) represents the first-order delay circuit. The first-order delay circuit 23 illustrated in FIG. 8 calculates the second term of formula (3).
In this case, if a condition Tv>>(Kb/M)1/2 is applied to formula (3), the entire control system illustrated in FIG. 8 has the gain characteristic indicated by the dotted line in FIG. 12. The gain margin of the mechanical resonance frequency (Kb/M)1/2 becomes larger. Further, the entire control system has the gain characteristic indicated by the solid line in FIG. 12 in a case where the rigidity of a working part of the feed-axis decreases. Thus, the conventional position control apparatus illustrated in FIG. 8 is effective in solving the problem of low frequency vibrations described in the conventional example illustrated in FIG. 5.
The time constants Tp and Tv of the respective first-order delay circuits 17 and 23 illustrated in FIG. 7 and FIG. 8 can be optimized in the following manner. It is useful to increase the time constants Tp and Tv to increase the gain margin of the mechanical resonance frequency (Kb/M)1/2 and stabilize the control system. However, if the gain margin is increased excessively, the control system deteriorates in responsiveness. More specifically, increasing the gain margin constitutes reducing the gain in the control band.
In some cases, the effect of suppressing the load change disturbance or the effect of reducing the position error in a transient response maybe lost. Accordingly, it is desired that the time constants Tp and Tv of respective first-order delay circuits 17 and 23 increase in response to a reduction in the mechanical resonance frequency (Kb/M)1/2; more specifically, in accordance with the degree of a reduction in the rigidity of a working part of the feed-axis.
FIG. 9 is a control block diagram illustrating a conventional circuit configuration capable of increasing the time constant Tp of the first-order delay circuit 17 in response to a reduction in the rigidity of a working part of the feed-axis. A subtracter 15 calculates a deflection Ps, which is a difference between the driven member position detection value Pl and the motor position detection value Pm. A deflection detector 16 calculates a time constant coefficient Kt that corresponds to the deflection Ps and then multiplies the time constant coefficient Kt by an initial time constant value Tp0 to generate the time constant Tp to be used by the first-order delay circuit 17.
In the present example, the time constant coefficient Kt is set to increase in proportion to an increase of the deflection Ps. In this case, the time constant Tp to be used in the first-order delay circuit 17 becomes larger when the deflection Ps becomes larger, because the time constant Tp is defined by Tp=Tp0·Kt.
If the relationship between the rigidity of a working part of the feed-axis and the deflection Ps is taken into consideration, the rigidity of a working part of the feed-axis is expressed using the spring having the spring constant Kb that connects the driven member to the motor. If the rigidity decreases; more specifically, if the coupling by the spring is weakened, the deflection Ps (i.e., the difference between the driven member position Pl and the motor position detection value Pm) becomes larger.
More specifically, the deflection detector 16 increases the time constant Tp of the first-order delay circuit 17, considering that the deflection Ps becomes larger when the rigidity of a working part of the feed-axis decreases.
The conventional circuit illustrated in FIG. 9 increases the time constant Tp of the first-order delay circuit 17 and, at the same time, reduces the gain Kp of the speed command calculator 3 in accordance with a reduction in the rigidity of a working part of the feed-axis. The deflection detector 16 calculates the coefficient K that corresponds to the deflection Ps. The deflection detector 16 multiplies the coefficient K by an initial gain value Kp0 to determine the gain Kp to be used in the speed command calculator 3. The coefficient K is set to have a value that decreases when the deflection Ps increases. In this case, the gain Kp becomes smaller when the deflection Ps becomes larger, because the gain Kp is defined by Kp=Kp0·K. More specifically, the deflection detector 16 decreases the gain Kp of the speed command calculator 3 when the rigidity of a working part of the feed-axis reduces.
In the state where the rigidity of a working part of the feed-axis is reduced, the entire control system has the gain characteristic illustrated in FIG. 11. However, when the time constant Tp of the first-order delay circuit 17 is increased in response to a reduction in the rigidity of a working part of the feed-axis, the entire control system illustrated in the block diagram of FIG. 7 has the gain characteristic indicated by the dotted line in FIG. 13. Further, when the gain Kp of the speed command calculator 3 is reduced, the entire control system illustrated in the block diagram illustrated in FIG. 7 has the gain characteristic indicated by the solid line in FIG. 13.
As a result, the gain margin of the mechanical resonance frequency (Kb/M)1/2 becomes larger. Thus, the system illustrated in FIG. 9 is effective in solving the problem of low frequency vibrations described in the conventional example illustrated in FIG. 5. At the same time, the system illustrated in FIG. 9 can prevent the gain margin from being secured excessively and prevent the responsiveness of the control system from deteriorating excessively, because the time constant Tp of the first-order delay circuit 17 and the gain Kp of the speed command calculator 3 are appropriately changed in response to a reduction in the rigidity of a working part of the feed-axis.
The conventional circuit configuration illustrated in FIG. 9 secures a sufficient gain margin of the mechanical resonance frequency (Kb/M)1/2 and suppresses low frequency vibrations by increasing the time constant Tp of the first-order delay circuit 17 or decreasing the gain Kp of the speed command calculator 3 in accordance with a reduction in the rigidity of a working part of the feed-axis. The reduction in the rigidity of a working part of the feed-axis can be detected based on an increase in the deflection Ps. However, the phenomenon that causes an increase in the deflection Ps is not limited to the above-described case where the rigidity of a working part of the feed-axis decreases or the case where the loading weight of a driven member increases.
A similar phenomenon may occur in response to an increase in the sliding friction acting on a driven member. If the deflection Ps increases in accordance with an increase in the sliding friction acting on a driven member, the gain margin of the mechanical resonance frequency (Kb/M)1/2 does not vary substantially. Therefore, it is unnecessary to increase the time constant Tp of the first-order delay circuit 17 or to reduce the gain Kp of the speed command calculator 3. On the other hand, increasing the time constant Tp or reducing the gain Kp of the speed command calculator 3 in this situation secures the gain margin excessively. As a result, the control system may deteriorate in responsiveness. On the contrary, when the deflection Ps decreases in accordance with a reduction of the sliding friction acting on the driven member, low frequency vibrations occur if the time constant Tp of the first-order delay circuit 17 is reduced or the gain Kp of the speed command calculator 3 is increased, although there is no variation in the gain margin of the mechanical resonance frequency (Kb/M)1/2.
A practical influence of the sliding friction is described in detail below. The position detection value Pl of a driven member can be expressed using the following formula (4), in which Fd represents the sliding friction acting on the driven member and Pm represents the motor position detection value. In formula (4), S represents a Laplacian operator.Pl(S)={Kb/(M·S2+D·S+Kb)}·Pm(S)−{1/(M·S2+D·S+Kb)}·Fd(S)   formula (4)
If a condition Fd=0 is applied to formula (4); more specifically, when the sliding friction acting on a driven member is ignored, formula (4) becomes equivalent to a spring model 28 of the block diagram illustrated in FIG. 6. More specifically, regardless of the presence of the sliding friction, the mechanical resonance frequency is equal to (Kb/M)1/2, which is substantially determined by the rigidity of a working part of the feed-axis and the loading weight of the driven member.
However, the position detection value Pl of a driven member is influenced by the sliding friction acting on the driven member. If driving at an extremely low frequency is presumed; i.e., S=0 in formula (4), formula (4) can be replaced by the following formula (5).Pl(S)=Pm(S)−{1/Kb}·Fd(S)   formula (5)
More specifically, the magnitude of the deflection Ps (i.e., the difference between the driven member position detection value Pl and the motor position detection value Pm) increases if the rigidity of a working part of the feed-axis decreases; namely, when the spring constant Kb becomes smaller, or when the sliding friction Fd becomes larger.
Further, the magnitude of the sliding friction Fd is variable depending on the speed of the driven member. For example, in a case where a sliding guide mechanism is provided to support and drive the driven member, if the moving speed is high, the driven member can slide on an oil film with less sliding friction. On the other hand, if the moving speed is low, the driven member is subjected to a frictional resistance of the oil film and therefore the sliding friction Fd increases.
Further, the magnitude of the sliding friction Fd is variable due to various factors (e.g., temperature and position of the driven member). Therefore, it is difficult to accurately detect the magnitude of the sliding friction Fd. More specifically, in a driving mechanism including a driven member subjected to a sliding friction that is variable, it is difficult to detect a reduction in the rigidity of a working part of the feed-axis based on the deflection Ps. The time constant Tp of the first-order delay circuit 17 cannot be determined appropriately.
Further, the conventional system illustrated in FIG. 9 secures a sufficient gain margin of the mechanical resonance frequency (Kb/M)1/2 and suppresses low frequency vibrations by adequately changing the time constant Tp of the first-order delay circuit 17 and the gain Kp of the speed command calculator 3. However, the control system greatly deteriorates in command responsiveness, although reducing the gain Kp is effective for stabilizing the control system.
Similar to FIG. 6, if it is assumed that the transfer characteristic of a portion ranging from the speed command Vc to the motor speed detection value Vm is equal to 1, the position deviation Pdif and the driven member position detection value Pl in the control system illustrated in FIG. 7 can be expressed by the following formulae (6) and (7) using the position command Pc. In formulae (6) and (7), S represents a Laplacian operator.Pdif(S)=Pc(S)·{S·(1+Tp·S)·(M·S2+D·S+Kb)}/{S·(1+Tp·S+Kp·Tp)·(M·S2+D·S+Kb)+Kp·Kb}  formula (6)Pl(S)=Pc(S)·{(1+Tp·S)·Kp·Kb}/{S·(1+Tp·S+Kp·Tp)·(M·S2+D·S+Kb)+Kp·Kb}  formula (7)If Tp=0 in formulae (6) and (7), the position deviation Pdif and the driven member position detection value Pl coincide with the transfer characteristic of the control system illustrated in FIG. 6.
To the contrary, if the time constant Tp of the first-order delay circuit 17 is greatly increased (Tp=∞), formulae (6) and (7) can be replaced by the following formulae (8) and (9).Pdif(S)={S/(S+Kp)}·Pc(S)   formula (8)Pl(S)={Kp/(S+Kp)}·{Kb/(M·S2+D·S+Kb)}·Pc(S)   formula (9)
This is the same as the case where the motor position detection value Pm is equal to the position feedback value Pd. Further, formula( 8) indicates that a control response band of the position control system is determined by the gain Kp of the speed command calculator 3. The motor position detection value Pm does not deteriorate in responsiveness even if the time constant Tp of the first-order delay circuit 17 is increased.
Further, formula (9) indicates that the response band of the driven member position detection value Pl is determined by the gain Kp of the speed command calculator 3 unless the rigidity of a working part of the feed-axis in the spring model 28 decreases too drastically to maintain a relationship Kp<(Kb/M)1/2. More specifically, although the deterioration in responsiveness of the driven member position detection value Pl is influenced by a reduction in the rigidity of a working part of the feed-axis, the amount of the influence is substantially ignorable because it is a variation suppressed by a first-order delay element of the gain Kp.
On the other hand, if the gain Kp of the speed command calculator 3 is reduced greatly (Kp=0), formula (6) can be replaced by the following formula (10).Pdif(S)=Pc(S)   formula (10)
Formula (10) indicates that the position control system does not respond at all. Reducing the gain Kp of the speed command calculator 3 is effective in suppressing low frequency vibrations that may occur when the rigidity of a working part of the feed-axis decreases. However, the motor position detection value Pm will deteriorate in responsiveness. Needless to say, the responsiveness of the driven member position detection value Pl further deteriorates, compared to that of the motor position detection value Pm, by an amount corresponding to the reduction in the rigidity of a working part of the feed-axis.
One of the problems to be solved by the present invention is that it is unable to detect a reduction in the rigidity of a working part of the feed-axis in a driving mechanism in which a driven member is subjected to a torque disturbance, such as sliding friction, because the magnitude of a deflection may change in accordance with a variation in the magnitude of the torque disturbance. Further, it is unable to adjust the time constant of a first-order delay circuit, which is required to calculate a position/speed feedback value, to an appropriate value according to the degree of reduction in the rigidity of a working part of the feed-axis. As a result, if an excessively large gain margin is secured, the control system may deteriorate in responsiveness. On the other hand, if the secured gain margin is smaller, low frequency vibrations may occur in a driven member.
An object of the present invention is to provide a position control apparatus that can detect a reduction in the mechanical resonance frequency that may occur in response to a reduction in the rigidity of a working part of the feed-axis or in response to an increase in loading weight of a driven member and, at least, can optimize the time constant of the first-order delay circuit according to resonance characteristics in such a way as to prevent the driven member from vibrating at low frequencies and minimize the reduction in responsiveness of the control system.